Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
1.1 kgk = ?

A 1.1 kg mass on a spring oscillates with a period of 0.8 s. Find the spring stiffness k.

m = 1.1 kgT = 0.8 s
k = N/m
2.Easy
4.2 kgk = ?

A 4.2 kg mass on a spring oscillates with a period of 0.4 s. Find the spring stiffness k.

m = 4.2 kgT = 0.4 s
k = N/m
3.Medium
2.1 kgk = 310 N/mA = 17 cmx = 4 cm

A 2.1 kg mass on a spring with k = 310 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its speed v when it is 4 cm from equilibrium.

m = 2.1 kgk = 310 N/mA = 17 cmx = 4 cm
v = m/s
4.Medium
L = 0.5 m

A simple pendulum has a length of 0.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.5 mg = 9.81 m/s²
T = s
5.Hard
0.3 kgk = 130 N/mA = 2 cm

A 0.3 kg mass on a spring with k = 130 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.3 kgk = 130 N/mA = 2 cm
vmax = m/s
6.Hard
1.6 kgk = 140 N/mA = 13 cm

A 1.6 kg mass on a spring with k = 140 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.6 kgk = 140 N/mA = 13 cm
E = J

Answer key

  1. 1. k = 67.85 N/m
  2. 2. k = 1036 N/m
  3. 3. v = 2.007 m/s
  4. 4. T = 1.419 s
  5. 5. vmax = 0.4163 m/s
  6. 6. E = 1.183 J

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